How to manually achieve a motion blur effect on a object in the compositor?
Use the directional blur node.

Form the blender manual:

Iterations
Controls how may times the image is duplicated to create the blur effect. Higher values give smoother results.
Wrap
Wraps the image on the X and Y axis to fill in areas, that become transparent from the blur effect.
Center X, Y
Sets the position where the blur center is. This makes a difference if the angle, spin, and/or zoom are used.
Distance
How large the blur effect is.
Angle
Image is blurred at this angle from the center.
Spin
Rotates the image each iteration to create a spin effect, from the center point.
Zoom
Scales the image each iteration, creating the effect of a zoom.